Chapter 2. Estimation of Wind Load Effects

Wind forms the predominant source of loads, in tall freestanding structures – like

chimneys. The effect of wind on these tall structures can be divided into two

components, known respectively as

! along-wind effect

! across-wind effect

Along-wind loads are caused by the ‘drag’ component of the wind force on the

chimney, whereas the across-wind loads are caused by the corresponding ‘lift’

component. The former is accompanied by ‘gust buffetting’ causing a dynamic response

in the direction of the mean flow, whereas the latter is associated with the phenomenon

of ‘vortex shedding’ which causes the chimney to oscillate in a direction perpendicular

to the direction of wind flow. Estimation of wind effects therefore involves the

estimation of these two types of loads.

2.1 Along Wind Effects

Along-wind effect is due to the direct buffeting action, when the wind acts on the

face of a structure. For the purpose of estimation of these loads the chimney is modeled

as a cantilever, fixed to the ground. The wind is then modeled to act on the exposed face

of the chimney causing predominant moments in the chimney. Additional complications

arise from the fact that the wind does not generally blow at a fixed rate. Wind generally

blows as gusts. This requires that the corresponding loads, and hence the response be

taken as dynamic. True evaluation of the along-wind loads involves modeling the

concerned chimney as a bluff body having incident turbulent wind flow. However, the

mathematical rigor involved in such an analysis is not acceptable to practicing

engineers. Hence most codes use an ‘equivalent static’ procedure known as the gust

factor method. This method is immensely popular and is currently specified in a number

of building codes including the IS (IS:4998) code. This process broadly involves the

determining of the wind pressure that acts on the chimney due to the bearing on the face

2

of the chimney, a static wind load. This is then amplified using the ‘gust factor’ to take

care of the dynamic effects.

This study involves the evaluation of the along-wind loads by using the methods

specified in a number of codes like

! CICIND (Model Code for Concrete Chimneys, 1998)

! ACI 307-95

! IS 4998 (Part 1) : 1992

2.1.1 Basic Design Wind speed

One of the primary steps to finding the along-wind loads is to get the basic

design wind speed. The determination of the effective wind pressure is based on the

basic wind speed. The basic wind speed (Vb) is defined (by the CICIND code) as the

mean hourly wind speed at 10m above the ground level in open flat country without

having any obstructions. This means that the wind speed is measured at a height of 10m

above the ground at the location of the chimney and is averaged over an hour. The ACI

code suggests a wind speed averaged over a period of the order of 20min to 1hr. The IS

code however uses the basic wind speed based on peak gust velocity averaged over a

short time interval of about three seconds. The value of the basic wind speed must be

established by meteorological measurement. Normally though it is not necessary to

actually do the measurement for a particular region. The values as suggested from

published Wind Maps specified by the codes may be used. Basic wind speeds generally

have been worked out for a return period of 50 yrs.

It may me noted that the ACI follows the FPS system and therefore in the

following discussion the formulae by the code appear different from the SI system of the

other two codes.

2.1.2 Wind Profile

Wind flow is retarded by frictional contact with the earth’s surface. The effect of

this retardation is diffused by turbulence in wind flow across a region known as the

‘atmospheric boundary layer’. The thickness of this boundary layer depends on the wind

speed, terrain roughness and angle of latitude. The rougher the terrain, the more

effective the retardation to the mean flow, and hence, greater is the gradient height. The

3

effect of this gradient is the wind flow now assumes a profile that varies with height

from 0 at the surface to the maximum at the end of the ‘atmospheric boundary layer’.

The variation of mean wind speed with height Vz is generally described by the

power law.

(2.1) Vz = Vb (Z / Zo)

Where Vz is the profile with respect to height. Vb is the basic wind speed, Z is

the height above ground level, Zo) is a height of the boundary layer and is the terrain

factor. The values of the various factors are specified by the respective codes.

The CICIND code suggests the following code for the purpose of evaluation of

the wind speed profile.

(2.2) V(z) = Vb k(z) kt ki

Where:

V(z) is the hourly mean wind speed at level z

z is the height above ground level

Vb is the basic wind speed specified

k(z) is given by the equation

(2.3) k(z) = ks (z / 10)

ks scale factor, equal to 1.0 in open flat country

is the terrain factor

kt topographical factor

ki interference factor

The ACI code gives the following formula for obtaining the Wind profiles

V(z) = (1.47)0.78(80/VR)

0.09 VR(z/33)

0.14

(2.4)

Where VR is the basic wind speed. The equation also converts from the basic

wind speed in mph to ft/s as required for the calculations.

The IS:875 however does not give a wind profile but gives a wind velocity at any

height Vz. (2.5) Vz = Vb k1 k2 k3

4

Where Vz is the required wind speed, Vb is the basic wind speed. k1 is a

probability factor (risk), k2 is the terrain, height and structure size factor,k3 is a

topography factor. The values of these factors can be gauged from the Tables given in

the IS code.

2.1.3 Design Wind Pressure

The obtained wind velocities are assumed to act on the face of the chimney. The

corresponding pressure on the surface has to be evaluated next. This is done with the

help of the drag coefficient. This coefficient is defined in a number of ways in all the

codes. The main concept however is that the square of the velocity acting at any point is

to be multiplied by this coefficient to get the pressure acting at that point. The

coefficient takes into account factors like – slenderness of the column, ribbed quality of

the surface, the effect of having a curved surface etc.

The wind pressure then is multiplied with the density of air and the exposed area

to get the actual static loads acting on the chimney.

The CICIND code calculates the loads with the following formula

wm(z) = 0.5 !a v(z)

2 CD d(z) (2.6)

Which is more than just the pressure calculation. However the term CD refers to

the coefficient that depends on the slenderness of the column. The value of this

coefficient depends on the h/d ratio and can be obtained from the code. It varies between

0.6 and 0.7 for change in the h/d ratio from 5 to 25. The term wm(z) is basically the

‘weight’ acting on the cantilever for which it has to be designed.

The Indian code converts the velocity profile into its corresponding pressure

profile with the help of the following formula

pz = 0.6 Vz2

(2.7)

The value of 0.6 is the drag coefficient specified.

5

The ACI code suggests a very similar function, however specifying the

coefficient to be 0.0013 as opposed to 0.6, mainly to keep it consisting with the FPS

system used by the code.

6

Figure 2.1 – Wind profile and Response

2.1.4 Force resultants

The pressure values obtained in the earlier case are then converted into the

corresponding force values. The chimney is idealized to be a vertical cantilever, fixed to

the ground. The load that acts can be takes as a continuous load acting on this cantilever.

The calculation of the force resultants of shear and moment are trivial.

In reality the base of the chimney is broad. Hence the shear resisting capacity of

the chimney is high. In fact shear also may manifest itself as moment due to the deep

beam effect. Hence the more important resultant to calculate here is the moment as

compared to either the shear or the axial force.

Moment

Wind

Profile

The moment at any point on the cantilever can be calculated by integrating the

moment from the end to that point. Hence the functions given to calculate the moment

too are integrals.

The CICIND code gives the following main formula for the purpose of

calculation of the gust factor moments in chimneys

"#

$h

mg zdzzwh

zGzw

0

2)(

)1(3)( (2.8)

where

G is the gust factor (will be looked into later)

h is the height of the top of the shell above the ground level

z is the height above the ground level

wm(z) is the mean hourly wind load per unit height at height z

The IS code gives two methods for the evaluation of along-wind loads on

chimneys, both of which are discussed below.

The IS simplified method

This method, as the name suggests, is a simple procedure to come up with the

load values for a given configuration. The formula suggested for this method is

Fz = pz.CD.dz (2.9)

Where the factor CD is to be taken as 0.8. This is actually a vast simplification of

the procedure outlined in the IS:875 which specifies the distribution of the value of the

drag coefficient around the periphery of the cylindrical shell. This method however does

not take into account the effect of the dynamic quality of the incident wind on the

chimney.

The second method given by the code is the random response method. The

equations for the same are given below and terms explained. The need and use of the

Gust factor however is discussed later.

"#

$H

zmzf zdzFH

z

H

gF

0

2

)1(3(2.10)

7

8

8

Where Fzf is the wind load in N/m height due to the fluctuating component of the

wind at height z. The whole load is given by

(2.11)

zfzmz FFF %$

The wind load due to the hourly mean wind component is given by

where pz gives the design pressure at hourly mean wind component and is

pbtained by the equation

zDzzm dCpF $ (2.12)

zVp z2

6.0$ (2.13)

In the equation for the fluctuating component of the wind load the gust factor G

is used. The equations and the concept involved are discussed later.

The ACI code gives the following code for the purpose of calculation of the

along-wind load. This code too divides the load due to the wind into two parts – the

mean load and the fluctuating component. The mean load is calculated by the formula

)()()()( zpzdzCzw dr$ (2.14)

Where the value

Cdr = 0.65 for z < h-1.5d(h)

Cdr = 1 for z > h-1.5d(h)

And the value of the mean pressure has been given.

The fluctuating load component has been taken equal to

3

' )(0.3)('

h

bMzGzw ww$ (2.15)

Where M is the base bending moment due to the constant load acting on the

chimney. It is basically an integral of the weight acting on the chimney multiplied with

the distance from the base. The Gust factor G is calculated by

& '86.0

47.0

1

)16(

)33(0.1130.0'

%%$

h

VTGw

(2.16)

For a preliminary design the Time period of oscillation can be calculated with

the help of an equation suggested by the code. However the code requires the time

period to be calculated with the help of dynamic analysis for the final design. Analysis

here was done by modeling the chimney using a program STRAP.

2.1.5 Dynamic Effects and the Gust Factor

All along-wind loads that act on the chimney are not due to the static wing

bearing on the surface of the chimney alone. There is a significant change in the applied

load due to the inherent fluctuations in the strength of wind that acts on the chimney. It

is not possible of feasible to take the maximum load that can ever occur due to wind

loads and design the chimney for the same. At the same time it is very difficult to

quantify the dynamic effect of the load that is incident on the chimney. Such a process

would be very tedious and time consuming. So most of the codes make use of the gust

factor to account for this dynamic loading. To simplify the incident load due to the mean

wind is calculated and the result is amplified by means of a gust factor to take care of the

dynamic nature of the loading.

The gust factor is defined as the ratio of the expected maximum moment M0 to

the mean moment Mm0 at the base of the chimney. It is accordingly denoted as G0 and is

referred to as the base gust factor.

The CICIND code gives the following formula for the calculation of the Gust

factor.

(ES

BgiG %%$ 21 (2.17)

Where g is peak factor with

vTvTg

e

elog2

577.0log2 %$

(2.18)

the turbulence intensity

hi 10log089.0311.0 #$ (2.19)

88.0

63.0

2651

#

))*

+

,,-

./0

123

4%$h

Bbackground turbulence (2.20)

9

83.0

42.0

2

1

21.01

3301

123

))*

+

,,-

.//0

1223

4%

//0

1223

4

$

hV

f

hV

f

E

b

benergy density

(2.21) spectrum

88.0

98.0

14.1

178.51

#

//

0

1

22

3

4//0

1223

4%$ h

V

fS

b

size reduction factor (2.22)

damping " is a fraction of the critical damping and is taken as 0.016. f1 is the

natural frequency in the first mode of vibration.

h is the height of the shell above the ground in m and Vb is the basic wind speed.

T is the sample period and v is effective cycling rate.

The equation for the Gust factor used by the ACI code is given earlier.

The IS code probably borrowed its gust factor equation from the CICIND code

as both the equations are remarkably similar. Only the names given to some of the

factors are different. The factors and the equations themselves are the same

A typical chimney of 250m was chosen to calculate the along-wind loads. The

dynamic analysis was done using a structural analysis program called STRAP.

2.1.6 Analysis using STRAP

For the purpose of analysis the chimney was modeled in STRAP. The chimney

was idealized into 32 components outside the ground and one component inside the

ground (to take care of fixity and the effect of the foundation), a total of 33 components.

The various components were taken to be cylindrical objects. Hence the chimney was

idealized as 33 hollow cylinders stacked upon each other.

The thickness of the components of the chimney were varied according the

thickness of the actual chimney at the middle of each section. A fixed joint was assumed

after 32 nodes.

For the purpose of dynamic analysis the weight data was calculated by the

program itself. This however was strictly not correct because there would be the

10

additional weight of the lining inside the chimney. Hence a lining of a layer of bricks

was assumed and the weight calculated by the program was corrected with a factor to

account for the weight of the lining. The calculation of the factors was done with the

help of a small program that actually calculated the volume ratios for the purpose.

The chimney itself was assumed to be of a standard dimensions and ratios as

given below.

Attribute Value

Height 250m

Height to Base Diameter 7

Top Diameter to Base Diameter 0.6

Base Diameter to base thickness 35

Top thickness to base thickness 0.4675

Table 2.1 – Chimney Attributes

The results of dynamic analysis of the modeled chimney are given below

Mode Time Period

1 0.2345

2 1.0266

3 2.4826

4 3.6286

5 4.4460

Table 2.2 – Results of dynamic analysis

These values of time periods of oscillations and the corresponding frequencies

(1/Time Period) were used for the calculations of the Gust factor.

2.1.7 Expected maximum moments

The moments were calculated for the model chimney assumed earlier and the

results are shown in the graph below

11

0

50

100

150

200

250

300

0 500 1000 1500 2000

CICIND ACI IS

Figure 2.2 – Moment profiles (comparative)

As is visible, there is considerable difference in the expected maximum base

moments of the chimney using the three codal methods.

Additionally the base gust factors for the three methods are given below

Code Base Gust factor

IS 1.85

CICIND 1.85

ACI 1.993

Table 2.3 – Base Gust factors (comparative)

2.2 Across Wind Effects

Recommendations for considering the across-wind loads have been included into

the codes only recently. In spite of considerable research the problem of accurately

predicting the across-wind response has to be fully resolved. Hence the CICIND code

does not take into account across-winds. For this study the codes used therefore were the

IS 4998(Part 1): 1992 and the ACI 307-95.

12

A tall body like the chimney is essentially a bluff body as opposed to a

streamlines one. The streamlined body causes the oncoming wind flow to go smoothly

past it and hence is not exposed to any extra forces. On the other hand the bluff body

causes the wind to ‘separate’ from the body. This separated flow causes high negative

regions in the wake region behind the chimney. The wake region is a highly turbulent

region that give rise to high speed eddies called vortices. These discrete vortices are

shed alternately giving rise to ‘lift forces’ that act in a direction perpendicular to the

incident wind direction.

13

Figure 2.3 – Across wind effect

These lift forces cause the chimney to oscillate in a direction perpendicular to the

wind flow.

2.2.1 Vortex Shedding

The phenomena of alternately shedding the vortices formed in the wake region is

called vortex shedding. This is the phenomena that gives rise to the across-wind forces.

This phenomena was reported by Strouhal, who showed that shedding from a

circular cylinder in a laminar flow is describable in terms a non-dimensional number Sn

called the Strouhal number.

CHIMNEY

velocityflowmean

cylinderofdiameterfrequencysheddingSn

__

___ 5$ (2.23)

The phenomena of vortex shedding and hence the across-wind loads depends on

a number of factors including wind velocity, taper factors etc., that are specified by the

codes. Codal estimation of the across-wind loads also involves the estimation of the

mode-shape of the chimney in various modes of vibration. This is obtained as follows.

2.2.2 Chimney Modeling and estimation of shape factor and time period

As discussed earlier dynamic analysis of the chimney was done using the

structural analysis program STRAP. A model chimney with the parameters shown

earlier was modeled and dynamic analysis performed on it. The required mode shapes

were obtained from the program itself.

The results from the analysis are given below with the normalized mode shapes

on the left and the corresponding frequencies of vibration on the right. It may be noted

that although four mode shapes have been assumed for the purpose of analysis, in reality

only the first two modes are actually active. This is because the wind velocity required

to make the chimney vibrate in higher mode shapes is very high.

Mode shapes 1 to 4

Frequencies:

Mode 1: 0.2345 hz

Mode 2: 1.0266 hz

Mode 3: 2.4826 hz

Mode 4: 3.6286 hz 0

5

10

15

20

25

30

35

-1.2 -0.7 -0.2 0.3 0.8

Figure 2.4 – Mode shapes

2.2.3 Estimation of Moments

The various codal methods for the purpose of estimation of along-wind loads are

as follows.

14

The IS code, gives two methods for the estimation of across-wind loads. These

are called respectively the simplified method and the random response method. The

amplitude of the vortex excited oscillation is to be calculated by the equation.

sin

L

H

zi

H

ziz

oiKS

C

dz

dzd

2

0

2

0

467

7

8 5

99

:

99

;

<

99

=

99

>

?

$

"

" (2.24)

Where #oi is the peak tip deflection due to vortex shedding in the ith mode of

vibration in m, CL = 0.16, H is the height in meters, Ksi is the damping parameter for the

ith

more of vibration, Sn strouhal number = 0.2 and $zi is the normalized mode shape.

Calculations of oscillation calculated using this formula are acceptable till 4

percent of the effective diameter. For values more that this the resultant is amplified

using a given formula.

Once this value is obtained the sectional shear force Fzoi and Bending moment

Mzoi at any height zo for the ith mode of vibration, as obtained as follows.

"$H

zo

ziziozoi dzmfF 786 2

1

24 (2.25)

"$H

zo

ziziozoi dzmfF 786 2

1

24 (2.26)

Where fi is the natural frequency in the ith mode of vibration and mz is the mass

per unit length of the chimney at section z in kg/m.

The mass damping factor Ksi required for the earlier equation is calculated using

the formula

2

2

d

mK sei

is @

A$ (2.27)

mei is the equivalent mass per unit length in kg/m in the ith

mode of vibration, %s

= 2&', and ' = 0.016 (structural damping factor), ( is the mass density of air taken as 1.2

kg/m3 and d is the effective diameter taken as average diameter over the top 1/3 height

of the chimney in m.

15

The equivalent mass per unit length in the ith

mode of vibration can be calculated

using the formula given below. It is basically dependant on the amount of mass that is

available given the mode shape.

"

"$

H

zi

H

ziz

ei

dz

dzm

m

0

2

0

2

7

7

(2.28)

The oscillation is caused by the wind. The mode in which the chimney vibrates is

decided by the wind speed. Higher modes need a higher wind speed for excitation.

Hence it is possible to know the wind velocities that causes shedding in the ith

mode. It is

done with the help of the following equation.

n

criS

dfV 1$ (2.29)

Since higher wind speeds are required to excite higher modes of vibration, it is

not necessary to consider all the modes of vibration for the purpose of design. All modes

which can be excited up to wind speeds of 10 percent above the maximum expected at

the height of the effective diameter shall be considered for subsequent analysis. If the

critical winds for any mode of vibration, exceeds the limits specified earlier, the code

allows the assumption that the problem of vortex excited resonance will not be a design

criteria for that and higher modes. In these cases across-wind analysis may not be

required.

The across-wind analysis using the random response method is also specified by

the code. The relevant expressions are given for chimneys of two types – those with

little or no taper and those with significant taper. Taper is defined as

H

ddtaper

topav )(2 #$ (2.30)

When the value of the taper is less than 1 in 50 (or 2 percent) the chimney is said

to have little taper.

For chimneys with little or no taper, the expression to calculate the modal

response at critical wind speed as given in equation 2.24 earlier

16

ei

azi

ein

L

oi

m

dkdz

H

m

Ld

S

HdC

22

2

22

1

1

)2(225.1

@B7

6@

6

7

8

#

:;<

=>?

%5

$

"

(2.31)

Where the RMS lift coefficient is taken as 0.12, correlation length in diameters is

taken as 1.0 and the aerodynamic damping coefficient is taken as 0.5.

Chimneys that are significantly tapered have the following equation

"#

$H

ei

aziziei

zeizeL

oi

m

dkdmS

t

LHdC

0

2222

1

4

2

2

@B76

677@

8 (2.32)

Where zei is the height in m at which a given expression is maximum in the ith

mode of vibration. The term in the expression is the power law exponent which was

discussed earlier with respect to the wind profiles. The value of this depends on the

Terrain Category and varies from 0.10 to 0.34.

The critical wind speed for exciting the mode of vibration is determined by the

equation.

n

ize

criS

dfV

1$ (2.33)

Calculations begin by first taking zei =H and progressively decreasing till a

maximum in #oi is observed. Also if the required velocity for excitation in any mode is

greater than the maximum velocity, the chimney will not be assumed to experience

much across-wind loads in that and higher modes. If this applies to the first mode of

vibration itself then the chimney has negligible across-wind loads.

The ACI code considers the across-wind loads due to vortex shedding for in the

design of chimneys when the critical velocity is between 0.5 and 1.3 Vzcr. Across-wind

loads are not considered outside this range.

Te critical velocity is calculated using the function.

t

crS

ufdV

)($ (2.34)

17

Where the St is the Strouhal number and is calculated using

//0

1223

4%$

)(log206.0333.025.0

ud

hS et

(2.35)

d(u) is the mean outside diameter of the upper 1/3 of the chimney in feet, and h is

the height above the ground level.

The peak base moment at the critical velocity if determined by the equation.

C D)*

+,-

.%

%

$

E

p

as

crLSa

Cud

h

LShudV

aCS

g

GM

)(

2

4)(

2

22

BB6E

(2.36)

Ma is evaluated over a range of wind speeds in the specified range of 0.5 to 1.3

Vcr to determine the maximum response. For values of velocity greater than Vcr the

value of Ma is multiplied with

4.1

1

)(

)(

3

44.1

9:

9;<

9=

9>?

)*

+,-

. ##

cr

cr

zV

zVV(2.37)

The values of the various terms are given in the code including the peak factor,

mode shape factor and specific gravity of air.

The code also gives a formula for the calculation of the time period in the second

mode of vibration, although the final design needs a dynamic analysis. The values

obtained from the STRAP program were used in this calculations.

The results of the analysis are given below

18

0

50

100

150

200

250

300

-400 -200 0 200 400 600 800

Mode 1 Mode 2

Figure 2.5 – IS Simplified method & Figure 2.6 – IS Random Response Method

0

50

100

150

200

250

300

-1000 -500 0 500 1000 1500

Mode 1 Mode 2

19

The first graph refers to the result of the IS simplified method, whereas the

second graph refers to the IS Random response method.

As can be seen from the graph the moments in the first mode of vibration are

very similar for both the methods of calculation, whereas the moments for the second

mode of vibration vary a lot. The moments obtained from the Random response method

are almost double that obtained using the simplified method. In fact the Random

response method given higher moments for the second mode of vibration and lower

moments for the first mode of vibration, as compared to the simplified method.

The base moments as calculated using the ACI method are given below

(All values MNm) Across-wind Along-wind Gust Factor Max Moment

Mode 1 125.46 432.98 1.8854 825.922

Mode 2 98.86 432.98 1.592 696.56

Table 2.4 – Base Moments (ACI)

It is seen that the values obtained using the ACI method are very small as

compared to the IS method. This is especially true of the across-wind loads.

2.2. Variation of moments with change in H by D ratio

An analysis was done to find the change in across-wind loads with change in

Height to Base diameter ratio.

For the purpose of the Analysis, Chimneys with the following parameters were

used

Height : 250 m

Height to Base diameter Ratio : 7, 9, 11, 12, 13, 15, 17

Top diameter to Base diameter Ratio : 0.6

Base diameter to Base thickness Ratio : 35

Top thickness to Base thickness Ratio : 0.4675

The following methods were employed for the same

1. IS Approximate Method

2. IS Random Response Method

3. ACI – 95 Method (Also CICIND approved)

20

Estimation of Free Vibration parameters like the mode-shapes the free

frequency and the Weight data for the calculations were calculated by modeling the

chimney in STRAP. The modeling was done with the chimney broken down into 32

elements. Vibration Analysis was done for modes 1 to 5 but only the first two were

required for the purpose of Moment calculations.

2.2.5 Conclusions from the variational analysis

! The Across-Wind Moments were inversely proportional to the H by D Ratio.

The Moments consistently increased with fall in the H/D Ratio for all methods of

estimation.

! The Approximate method of the IS code gave consistently higher moments as

compared to the Random Response Method for vibrations in the first mode.

! The Approximate method of the IS code gave consistently lower moments as

compared to the Random Response Method for vibrations in the second mode.

! The IS method gave higher moments in the second mode of vibration as

compared to the first mode in both its methods.

! The ACI method gave very small values as compared to the IS methods for the

base moment in all cases

! Anomalously the moments in the second mode were lower in the ACI method as

compared to those in the first mode.

All relevant Data can be found in the subsequent pages. It may be noted that the

higher moment curves correspond to lower H/D ratio.

21

0

5

10

15

20

25

30

35

0 2000 4000 6000

Figure 2.7 – IS Approximate Method – Mode 1

0

5

10

15

20

25

30

35

-10000 -5000 0 5000 10000

Figure 2.8 IS Approximate Method – Mode 2

22

0

5

10

15

20

25

30

35

0 1000 2000 3000 4000 5000

Figure 2.9 IS Random Response Method – Mode 1

0

5

10

15

20

25

30

35

-20000 -10000 0 10000 20000 30000

Figure 2.10 IS Random Response Method – Mode 2

23

H/d 7 9 11 12 13 15 17

Mode 1 641.15 340.566 204.425 144.783 114.783 77.271 55.244

Mode 2 411.482 225.483 142.764 107.867 87.404 59.786 42.523

Table 2.5 ACI Method (all modes)

Conclusion

The wind loads form the major sources for moments on Tall free standing

structures like chimneys. We have looked at the two kinds on wind-loads that act on

chimneys and also have presented the calculations for a standard chimney.

24